Numerical manifold method based on the method of weighted residuals

2004 ◽  
Vol 35 (6) ◽  
pp. 470-480 ◽  
Author(s):  
S. Li ◽  
Y. Cheng ◽  
Y.-F. Wu
Keyword(s):  
Numerical Manifold Method ◽  
Weighted Residuals ◽  
Method Of Weighted Residuals ◽  
Numerical Manifold

Solving of Partial Differential Equations by Numerical Manifold Method with Partially Overlapping Covers

2014 ◽  
Vol 638-640 ◽  
pp. 1737-1740
Author(s):  
Ya Qi Gong ◽  
Qin Chen ◽  
Yong Feng Qi
Keyword(s):  
Posteriori Error ◽  
Numerical Manifold Method ◽  
Weighted Residuals ◽  
Highly Oscillatory ◽  
Solution Increase ◽  
Numerical Manifold ◽  
Practical Field ◽  
Error Method ◽  
General Method ◽  
Cover Function

Governing equations of 1D high-order numerical manifold method with partially overlapping covers have been deduced by the general method of weighted residuals. By using the proposed method, a highly oscillatory differential equation has been solved. In addition, a posteriori error method is adopted for evaluating the accuracy of the algorithm. Meanwhile, several factors affect the accuracy are also discussed. The results indicate that accuracy of solution increase with the decrease of overlapping ratio and the order of cover function. When higher order cover function such as 6th is used, higher accuracy will matched even for second derivative of unknowns. This paper attempts to enrich the theory and practical field of the NMM.

scholarly journals Direct Simulation of Low-Re Flow around a Square Cylinder by Numerical Manifold Method for Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhengrong Zhang ◽  
Xiangwei Zhang
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Numerical Manifold Method ◽  
Square Cylinder ◽  
Navier Stokes Equations ◽  
Weighted Residuals ◽  
Numerical Tests ◽  
Incompressible Viscous Flow ◽  
Numerical Manifold

Numerical manifold method was applied to directly solve Navier-Stokes (N-S) equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. As an application, mixed cover 4-node rectangular manifold element has been used to simulate the incompressible viscous flow around a square cylinder in a channel. Numerical tests illustrate that NMM is an effective and high-order accurate numerical method for incompressible viscous flow N-S equations.

scholarly journals Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

2021 ◽  
Vol 133 ◽  
pp. 104070
Author(s):  
Xian-yang Yu ◽  
Tao Xu ◽  
Michael J. Heap ◽  
Patrick Baud ◽  
Thierry Reuschlé ◽  
...  
Keyword(s):  
Time Dependent ◽  
Numerical Manifold Method ◽  
Deformation And Failure ◽  
Numerical Manifold

The variational principles and application of nonlinear numerical manifold method

2000 ◽  
Vol 21 (12) ◽  
pp. 1401-1406 ◽  
Author(s):  
Luo Shao-ming ◽  
Zhang Xiang-wei ◽  
Cai Yong-chang
Keyword(s):  
Variational Principles ◽  
Numerical Manifold Method ◽  
Numerical Manifold
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